This is a pretty difficult question to answer due to the very different nature of the empires' military situations, and more relevant to this sub, this question's nature as a counterfactual (ie didn't happen historically).

As noted in the sub rules

Questions should be about what did happen, not what could have happened. Questions of that type should be posted in r/HistoricalWhatIf.

You might do better asking this question in /r/HistoricalWhatIf or even /r/whowouldwin while pming some of the people on the /r/AskHistorians flare list such as the people with Military History Flares, European History Flares, and Asian History Flares as they might be willing to stage a debate in the previously mentioned subreddits (or whatever space you prefer).

EDIT: I forgot to mention that you will have to be more specific on the nature of the conflict between them as since real life geography would (and did) prevent such a conflict from taking place so you would have to create a scenario in which they are able to reach one another by land or sea while also determining how to make the scenario a fair setup to display the military prowess of each empire.

EDIT 2: I also forgot to mention that many of the flared users have good knowledge on things outside of their flares, for example /u/Tiako has a good background on Imperial China even though his flare is for Roman Archaeology. The flares denote people who have extremely in depth understanding of the flared fields with extensive sources and expert interpretations of those sources and events of the day. Make sure to ask around alot of the flared users to get the best possible background on these empires and their war capabilities.

Hello. Post has been removed, as it asks for speculation about a "what if" scenario, which is not permitted in this sub. (as described by /u/OldWorldGlory)